Nanobursa
In materials science and nanotechnology, a nanobursa (also nanobursa mesh) is a class of hierarchically graded, nanofibrous composite material in which sequential layers of porous polymeric nanofibers encapsulate carbon nanotubes (CNTs) that are surface-functionalized with distinct metal nanoparticles in each layer. The name is derived from the Latin bursa ("sac" or "pouch"), reflecting the encapsulating, sac-like relationship of the polymeric shell around the nanotube core. The material was introduced in 2014 by researchers at the Stevens Institute of Technology (Hoboken, New Jersey), with Dilhan M. Kalyon as the corresponding Author and principal investigator.
Nanobursa meshes are fabricated by a hybrid process combining twin-screw extrusion with electrospinning, enabling continuous, industrially-scalable production. Demonstrated realizations include graded layers bearing palladium (Pd), cobalt (Co), silver (Ag), and platinum (Pt) nanoparticles. Principal targeted application domains are heterogeneous catalysis (notably hydrocarbon oxidation), filtration, and tissue engineering scaffolds.
Nomenclature and etymology
The term nanobursa is a portmanteau of the prefix nano- (from Greek nanos, dwarf; denoting the nanometer length-scale of the constituent fibers and tubes) and the Turkish noun bursa (pouch, purse). The anatomical analogy is apt: just as a bursa is a fluid-filled sac that cushions and encloses anatomical structures, each fiber of a nanobursa mesh encloses and protects a CNT core while simultaneously presenting a functionalized interface to the surrounding medium. The qualifier mesh refers to the nonwoven, interlaced architecture of the electrospun fiber mat.
The associated analytical representation used to characterize the rheological behavior of the precursor polymer–CNT suspension and, by extension, to optimize the electrospinning process, is termed the Mooney–Kalyon plot (by analogy with the Mooney–Rivlin plot of rubber elasticity). In this linearization, a suitably normalized stress measure is plotted against a reciprocal strain variable to extract material constants from slope and intercept, exactly as in the classical Mooney–Rivlin framework applied to elastomers.
Twin-screw extrusion / electrospinning (TSEE) hybrid process
Conventional electrospinning operates by applying a high electric field (typically 10–30 kV over a 10–20 cm gap) across a polymer solution or melt delivered through a capillary needle, drawing a charged jet that attenuates into fibers collected on a grounded substrate. It lacks inherent capacity for solids conveying, compounding, melting of high-viscosity resins, or controlled dispersion of nanoparticulate fillers.
The TSEE process, pioneered at Stevens Institute, integrates a co-rotating twin-screw extruder as the front end of an electrospinning system. The extruder provides:
- Solids conveying and metered feeding of CNT-loaded polymer granules;
- Dispersive and distributive mixing via kneading disc elements to de-agglomerate CNT clusters;
- Precise temperature profiling and devolatilization;
- Controlled pressurization to deliver the melt/solution uniformly to a multi-nozzle spinneret.
The multi-nozzle spinneret is necessary to achieve throughputs at industrially relevant rates, since the volumetric flow rate per nozzle in electrospinning is severely limited by hydrodynamic and electrostatic stability constraints (see §Electrospinning jet stability below).
Graded nanobursa meshes are formed by sequentially collecting layers produced from different CNT-suspension feedstocks, each bearing a distinct metallic nanoparticle type, on the same rotating drum collector. This yields a stratified, functionally graded architecture.
Metal nanoparticle functionalization of CNTs
Before incorporation into the polymer melt, multi-walled CNTs (MWCNTs) are surface-functionalized. A representative sequence is:
- Acid treatment (H₂SO₄/HNO₃ mixture, typical volume ratio 3:1, 60–80 °C, 1–4 h) to introduce carboxyl (–COOH) and hydroxyl (–OH) surface groups;
- Chelation of metal precursor salts (e.g., PdCl₂, CoCl₂, AgNO₃, H₂PtCl₆) to the oxidized surface;
- Chemical reduction (NaBH₄, hydrazine, or thermal) to generate metallic nanoparticles anchored to the CNT wall.
The resulting nanoparticle-on-tube structures are then dispersed in a polymeric carrier (e.g., polycaprolactone, PCL) prior to TSEE processing.
Structural description and length scales
A nanobursa mesh occupies multiple length scales simultaneously:
Structural element |
Characteristic dimension |
Role |
|---|---|---|
MWCNT core diameter |
20–30 nm |
Mechanical reinforcement; catalytic support |
Metal nanoparticle diameter |
2–10 nm |
Active catalytic sites |
Polymeric nanofiber diameter |
200–2000 nm |
Matrix; encapsulant; porosity control |
Mesh thickness (per layer) |
10–200 μm |
Graded functional zone |
Total mesh area (lab scale) |
cm2 – dm² |
Scalable via multi-nozzle TSEE |
The porosity of the nonwoven mat is governed by the fiber diameter distribution and mat basis weight, and typically falls in the range 60–90% void fraction, providing high specific surface area and low mass-transfer resistance.
Electrospinning jet instability and fiber diameter
The transition from a steady cone-jet (Taylor cone) to an electrically driven bending instability determines the final fiber diameter. The electric field strength E at the capillary tip of radius R charged to potential V relative to a collector at distance d is approximated by
$$E_{\mathrm{tip}} \approx \frac{V}{2R \ln(4d/R)}$$
The critical condition for jet ejection (Taylor cone formation) requires that the Maxwell stress exceed the surface tension restoring force:
$$\frac{\varepsilon_0 E^2}{2} \geq \frac{2\gamma}{R_{\mathrm{jet}}}$$
where ε0 is the permittivity of free space, γ is the polymer solution surface tension, and Rjet is the jet radius at the onset of instability. Solving for the jet radius:
$$R_{\mathrm{jet}} = \frac{4\gamma}{\varepsilon_0 E^2}$$
The final fiber diameter df, accounting for viscoelastic stretching and solvent evaporation, scales as
$$d_f \sim \left(\frac{Q \eta}{\pi \varepsilon_0 E^2}\right)^{1/3}$$
where Q is the volumetric flow rate per nozzle, η is the apparent viscosity of the spinning solution, and E is the applied electric field. This relationship predicts that increasing the applied voltage (raising E) or reducing the flow rate reduces the fiber diameter, consistent with experimental observations on PCL–CNT nanobursa precursor suspensions.
Rheology of CNT-loaded polymer suspensions
The precursor suspension of CNTs dispersed in a polymer carrier is a non-Newtonian fluid. For concentrated suspensions exhibiting a yield stress τy, the Herschel–Bulkley model is appropriate:
γ̇ = 0, |τ| ≤ τy
$$\boldsymbol{\tau} = \left(\frac{\tau_y}{\dot{\gamma}} + K \dot{\gamma}^{n-1}\right)\dot{\boldsymbol{\gamma}}, \quad |\boldsymbol{\tau}| > \tau_y$$
where K is the flow consistency index, n is the flow behavior index (n < 1 for shear-thinning behavior typical of CNT suspensions), and $\dot{\gamma} = |\dot{\boldsymbol{\gamma}}|$ is the magnitude of the rate-of-strain tensor $\dot{\boldsymbol{\gamma}} = \nabla\mathbf{v} + (\nabla\mathbf{v})^T$.
For the twin-screw extrusion stage, the relevant dimensionless number is the Deborah number
$$\mathrm{De} = \frac{\lambda_r \dot{\gamma}_{\mathrm{screw}}}{\mathcal{L}/\mathcal{U}}$$
where λr is the terminal relaxation time of the melt, γ̇screw is the characteristic shear rate imposed by the screw, ℒ is a characteristic length of the die/nozzle, and 𝒰 is the mean velocity. Optimal dispersion of CNT agglomerates requires De ≫ 1 in the kneading zones.
The Mooney–Kalyon plot
By analogy with the linearization introduced by Melvin Mooney (1940) for rubber elasticity, wherein a normalized stress T* plotted against β = 1/α (reciprocal stretch) yields the material constants C1 and C2 from intercept and slope respectively, an analogous linearization termed the Mooney–Kalyon plot, is introduced for the rheological characterization of nanobursa precursor suspensions undergoing steady simple shear.
Define the reduced apparent viscosity
$$\eta^{*}_{\mathrm{MK}} := \frac{\tau - \tau_y}{\dot{\gamma}}$$
and the reciprocal shear rate variable
$$\beta_{\mathrm{MK}} := \frac{1}{\dot{\gamma}}$$
Then, for a Herschel–Bulkley fluid,
ηMK* = Kγ̇n − 1 = KβMK1 − n
Taking logarithms:
ln ηMK* = ln K + (1−n)ln βMK
A plot of ln ηMK* versus ln βMK yields a straight line whose slope gives (1−n) and whose intercept gives ln K. This is the Mooney–Kalyon plot for nanobursa precursor suspensions.
Formally, the analogy with the Mooney–Rivlin framework for hyperelastic solids is structural: just as the Mooney–Rivlin plot
$$T^{*}_{11} = 2C_1 + 2C_2 \beta, \quad \beta = \frac{1}{\alpha}$$
extracts the constants C1 (intercept) and C2 (slope) governing the strain energy density function
W = C1(Ī1−3) + C2(Ī2−3)
the Mooney–Kalyon plot extracts the rheological parameters K and n governing the viscoplastic constitutive equation of the CNT-laden nanobursa precursor. In both cases the key insight is a linearization that reduces a nonlinear constitutive relationship to a straight-line fit on suitably chosen axes, with slope and intercept directly yielding the material constants.
Catalytic reaction model: hydrocarbon oxidation
The primary demonstrated application of the nanobursa mesh in catalysis is the oxidation of hydrocarbons. A generic complete oxidation reaction is
$$\mathrm{C}_x\mathrm{H}_y + \left(x + \frac{y}{4}\right)\mathrm{O}_2 \xrightarrow{\mathrm{Pd/Pt}} x\,\mathrm{CO}_2 + \frac{y}{2}\,\mathrm{H}_2\mathrm{O}$$
The catalytic rate per unit geometric area of the nanobursa mesh is modeled using a Langmuir–Hinshelwood mechanism. Denoting the hydrocarbon partial pressure as pHC and oxygen partial pressure as pO2, the surface reaction rate rs (mol m⁻² s⁻¹) is
$$r_s = \frac{k_s(T)\, K_{\mathrm{HC}}\, p_{\mathrm{HC}}\, K_{\mathrm{O}_2}\, p_{\mathrm{O}_2}}{(1 + K_{\mathrm{HC}}\, p_{\mathrm{HC}} + K_{\mathrm{O}_2}\, p_{\mathrm{O}_2})^2}$$
where ks(T) is the surface rate constant following an Arrhenius temperature dependence
$$k_s(T) = A\,\exp\!\left(-\frac{E_a}{R T}\right)$$
with A the pre-exponential factor, Ea the activation energy, R the universal gas constant, and T absolute temperature. KHC and KO2 are adsorption equilibrium constants for the hydrocarbon and oxygen, respectively.
The effectiveness factor ηeff of the nanobursa mesh accounts for intrafiber mass-transfer limitations. For a flat slab geometry of half-thickness L,
$$\eta_{\mathrm{eff}} = \frac{\tanh(\phi)}{\phi}$$
where ϕ is the Thiele modulus
$$\phi = L\sqrt{\frac{k_s a_s}{D_{\mathrm{eff}}}}$$
Here as is the specific surface area of the metallic nanoparticles per unit volume of the fiber (m2 m⁻³), and Deff is the effective diffusivity of the reactant within the porous fiber, estimated using
$$\frac{1}{D_{\mathrm{eff}}} = \frac{1}{D_{\mathrm{mol}}} + \frac{1}{D_K}$$
where Dmol is the bulk molecular diffusivity and $D_K = \frac{d_p}{3}\sqrt{\frac{8 R T}{\pi M}}$ is the Knudsen diffusivity with dp the mean pore diameter and M the molar mass of the diffusing species.
The overall volumetric conversion rate in a differential reactor element of mesh volume dV is
rvol = ηeff rs as ρfiber (1−ε) dV
where ε is the mesh void fraction and ρfiber is the skeletal density of the fiber material.
Graded layer architecture and optimization
The performance of a multi-layer nanobursa mesh (with N layers, each bearing a different metal ℳi at concentration ci) can be described by a transfer-matrix formalism. Let x(i) denote the state vector (reactant concentration, temperature) at the inlet of layer i. Then
x(i+1) = Ti(x(i); ci, df(i), εi)
where Ti is the layer transfer operator encoding the species and energy balances for that layer. The overall performance objective (e.g., total conversion X) is
$$X = 1 - \frac{[\mathrm{HC}]_{\mathrm{out}}}{[\mathrm{HC}]_{\mathrm{in}}} = \mathcal{F}\!\left(\{\mathbf{T}_i\}_{i=1}^N\right)$$
Optimization of the layer sequence—including the choice of metal identity, nanoparticle loading, fiber diameter, and void fraction for each layer—is a combinatorial problem that can be cast as
$$\max_{\{c_i,\, d_f^{(i)},\, \varepsilon_i,\, \mathcal{M}_i\}}\; X \quad \text{subject to} \quad \sum_{i=1}^N m_i \leq m_{\mathrm{total}},\quad \Delta P \leq \Delta P_{\max}$$
where mi is the mass of layer i and ΔP is the total pressure drop across the mesh, approximated for the fibrous medium by the Kozeny–Carman equation:
$$\Delta P = \frac{180\,\mu\, u_0\, L_{\mathrm{total}}}{d_f^2}\,\frac{(1-\varepsilon)^2}{\varepsilon^3}$$
where μ is the fluid dynamic viscosity, u0 is the superficial velocity, and Ltotal is the total mesh thickness.
Mechanical properties
The elastic modulus Emesh of an electrospun nonwoven mat composed of isotropically distributed fibers of modulus Ef and volume fraction φf = (1−ε) follows from the Cox shear-lag model adapted to fibrous networks:
$$E_{\mathrm{mesh}} = \frac{E_f \varphi_f}{6}\left[1 - \frac{\tanh(\beta_{\mathrm{Cox}} l/2)}{\beta_{\mathrm{Cox}} l/2}\right]$$
where l is the fiber segment length between junctions, and
$$\beta_{\mathrm{Cox}} = \sqrt{\frac{2 G_m}{\ln(R_c/r_f)\, E_f \pi r_f^2}}$$
with Gm the shear modulus of the surrounding medium (here effectively air, so Gm → 0 and the Cox correction reduces to unity for isolated fibers), Rc the mean center-to-center inter-fiber spacing, and rf = df/2 the fiber radius.
The addition of MWCNTs (at weight fraction wCNT) to the polymer matrix increases both fiber modulus and ultimate strength. A rule-of-mixtures-based Halpin–Tsai estimate for the fiber modulus gives
$$E_f = E_{\mathrm{poly}}\,\frac{1 + \zeta\, \eta_{\mathrm{HT}}\, V_{\mathrm{CNT}}}{1 - \eta_{\mathrm{HT}}\, V_{\mathrm{CNT}}}$$
where VCNT is the CNT volume fraction, ζ = 2(lCNT/dCNT) is the shape factor proportional to the CNT aspect ratio, and
$$\eta_{\mathrm{HT}} = \frac{(E_{\mathrm{CNT}}/E_{\mathrm{poly}}) - 1}{(E_{\mathrm{CNT}}/E_{\mathrm{poly}}) + \zeta}$$
Experimental uniaxial tensile data for PCL meshes have confirmed an increase in ultimate tensile strength from approximately 0.47 MPa (pure PCL) to 0.79 MPa upon incorporation of inorganic nanoparticles at 35 wt%, consistent with the Halpin–Tsai trend.
Filtration theory
For filtration applications (including antiviral or antimicrobial meshes), the single-fiber efficiency Esf of a cylindrical fiber of diameter df collecting particles of diameter dp is given by the sum of independent capture mechanisms:
Esf = ER + EI + ED + EER
where:
- $E_R = \left(\frac{d_p}{d_f}\right)^2 \cdot f(K_u)$ — interception efficiency, with $K_u = -\tfrac{1}{2}\ln\varphi_f - \tfrac{3}{4} + \varphi_f - \tfrac{\varphi_f^2}{4}$ the Kuwabara hydrodynamic factor;
- $E_I = \frac{St}{St + \pi/2}$ — inertial impaction, with Stokes number $St = \frac{\rho_p d_p^2 u_0}{18\mu d_f}$;
- ED = 2.9Ku−1/3Pe−2/3 + 0.624Pe−1 — diffusional capture, with Péclet number $Pe = \frac{u_0 d_f}{D_B}$ and Brownian diffusion coefficient $D_B = \frac{k_B T\, C_c}{3\pi\mu d_p}$ (Cc = Cunningham slip correction);
- EER — electrostatic capture (non-zero when fibers or particles carry net charge).
The overall fractional penetration of the nanobursa mesh of thickness L is
$$P = \exp\!\left(-\frac{4\,\varphi_f\, E_{\mathrm{sf}}\, L}{\pi\, d_f}\right)$$
and the filtration efficiency is ℰ = 1 − P. The presence of metal nanoparticles (notably Ag) on the CNT surface contributes an additional biocidal mechanism that does not appear directly in the mechanical filtration equation above.
Heterogeneous catalysis
The primary application demonstrated in the original nanobursa publication is catalytic hydrocarbon oxidation. The graded architecture allows sequential or cooperative catalytic action: for example, a Pd-rich upstream layer initiates partial oxidation, while a downstream Pt-rich layer drives complete combustion to CO₂ and H₂O. The mathematical framework for this is the layer transfer operator formalism described above.
Filtration and respiratory protection
By incorporating antiviral nanoparticles (Ag, Au, Pt, Pd) into electrospun PCL nanofibers produced by TSEE, nanobursa type meshes have been proposed as high-performance membrane layers for N95-class respirators. The sub-200-nm fiber diameters accessible via TSEE yield higher single-fiber efficiencies in the most penetrating particle size range (MPPS, approximately 100–300 nm) compared with conventional melt-blown polypropylene webs (fiber diameter typically 1–10 μm).
Tissue engineering and biomedical scaffolds
The TSEE platform that underlies nanobursa fabrication has been applied to the production of graded tissue engineering scaffolds, including:
- Functionally graded PCL / β-tricalcium phosphate (β-TCP) scaffolds for osteochondral interface Tissue engineering;
- Shell-core bi-layered scaffolds for engineering of vascularized osteon-like bone structures.
In biomedical contexts the encapsulation of CNTs within the polymeric shell of the nanobursa fiber serves the dual purpose of exploiting CNT mechanical reinforcement while limiting direct biological exposure to bare CNT surfaces, which carry cytotoxicity concerns.
Comparison with related materials
Material |
Fabrication |
Typical fiber diameter |
Graded composition |
Active nanoparticles |
|---|---|---|---|---|
Nanobursa mesh |
TSEE (twin-screw extrusion + electrospinning) |
200–2000 nm |
Yes (sequential layers) |
Pd, Co, Ag, Pt on CNTs |
Electrospun nanofiber mat |
Conventional electrospinning |
100–5000 nm |
Limited |
Blended only |
Melt-blown nonwoven |
Melt blowing |
1–10 μm |
No |
None (typically) |
Buckypaper |
Vacuum filtration of CNT suspension |
N/A (CNT mat) |
No |
Functionalized CNTs |
Graded TCP/PCL scaffold |
TSEE |
200–2000 nm |
Yes (concentration gradient) |
Calcium phosphate nanoparticles |
See also
- Electrospinning
- Carbon nanotube
- Hyperelastic material
- Mooney–Rivlin solid
- Herschel–Bulkley fluid
- Filtration
- Tissue engineering
Further reading
- Erisken, C., Kalyon, D. M., and Wang, H., 2008, "Functionally and continuously graded electrospun polycaprolactone and β-tricalcium phosphate nanocomposites for interface tissue engineering applications," Biomaterials, 29, 4065–4073.
- Senturk-Ozer, S., Ward, D., Gevgilili, H., and Kalyon, D., 2013, "Dynamics of electrospinning of poly(caprolactone) via hybrid twin screw extrusion and electrospinning and properties of electrospun fibers," Polymer Engineering and Science, 53(7), 1463–1474.
- Fridrikh, S. V., Yu, J. H., Brenner, M. P., and Rutledge, G. C., 2003, "Controlling the fiber diameter during electrospinning," Physical Review Letters, 90, 144502.
- Mooney, M., 1940, "A theory of large elastic deformation," Journal of Applied Physics, 11(9), 582–592.
- Rivlin, R. S., 1948, "Large elastic deformations of isotropic materials. IV.," Philosophical Transactions of the Royal Society of London. Series A, 241(835), 379–397.